Primary School Mathematics Year 3 to 6

Maths Tutor Melbourne

Mis Sch 2

Year 3 Mathematics

Elaborations

    1. Investigate the conditions required for a number to be odd or even and identify odd and even numbers (VCMNA129)
      • identifying even numbers using skip counting by twos or by grouping even collections of objects in twos
      • explaining why all numbers that end in the digits 0, 2, 4, 6 and 8 are even and that numbers ending in 1, 3, 5, 7 and 9 are odd
    2. Recognise, model, represent and order numbers to at least 10 000 (VCMNA130)
      • placing four-digit numbers on a number line using an appropriate scale
      • reproducing numbers in words using their numerical representations and vice versa
    3. Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems (VCMNA131)
      • recognising that 10 000 equals 10 thousands, 100 hundreds, 1000 tens and 10 000 ones
      • justifying choices about partitioning and regrouping numbers in terms of their usefulness for particular calculations
    4. Recognise and explain the connection between addition and subtraction (VCMNA132)
      • demonstrating the connection between addition and subtraction using partitioning or by writing equivalent number sentences
      • solving simple word problems involving addition or subtraction
    5. Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for computation (VCMNA133)
      • recognising that certain single-digit number combinations always result in the same answer for addition and subtraction, and using this knowledge for addition and subtraction of larger numbers
      • extending strategies for addition and subtraction such as 14 + 8 + 6 = 14 + 6 + 8 = 28 and 54 – 28 = 2 + 20 + 4
      • combining knowledge of addition and subtraction facts and partitioning to aid computation. For example, 57 + 19 = 57 + 20 – 1
    6. Recall multiplication facts of two, three, five and ten and related division facts (VCMNA134)
      • establishing multiplication facts using number sequences
      • using strategies to recall the multiplication and related division facts for the twos, threes, fives and tens
    7. Represent and solve problems involving multiplication using efficient mental and written strategies and appropriate digital technologies (VCMNA135)
      • writing simple word problems in numerical form and vice versa
      • using technology to check the solution and reasonableness of the answer

Fractions and decimals Elaborations

    1. Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole (VCMNA136)
      • partitioning areas, lengths and collections to create halves, thirds, quarters and fifths, such as folding the same sized sheets of paper to illustrate different unit fractions and comparing the number of parts with their sizes
      • locating unit fractions on a number line
      • recognising that in English the term ‘one third’ is used (order: numerator, denominator) but in other languages, such as Japanese for example, this concept may be expressed as ‘three parts, one of them’ (order: denominator, numerator)

Money and financial mathematics Elaborations

    1. Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents (VCMNA137)
      • recognising the relationship between dollars and cents, and that not all countries use these denominations and divisions. For example, the Japanese Yen

Patterns and algebra Elaborations

    1. Describe, continue, and create number patterns resulting from performing addition or subtraction (VCMNA138)
      • identifying and writing the rules for number patterns
      • describing a rule for a number pattern, then creating the pattern
    2. Use a function machine and the inverse machine as a model to apply mathematical rules to numbers or shapes (VCMNA139)
      • finding and describing simple rules in words to solve problems
      • using simple function machines to represent and apply a process or the inverse process, such as increase or decrease the value of a number by a specified amount


Year 4 Mathematics

Number and Algebra

Number and place value

    1. Investigate and use the properties of odd and even numbers (VCMNA151)
    2. Recognise, represent and order numbers to at least tens of thousands (VCMNA152)
    3. Apply place value to partition, rearrange and regroup numbers to at least tens of thousands to assist calculations and solve problems (VCMNA153)
    4. Investigate number sequences involving multiples of 3, 4, 6, 7, 8, and 9 (VCMNA154)
    5. Recall multiplication facts up to 10 × 10 and related division facts (VCMNA155)
    6. Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (VCMNA156)

Fractions and demicals

    1. Investigate equivalent fractions used in contexts (VCMNA157)
    2. Count by quarters, halves and thirds, including with mixed numerals. Locate and represent these fractions on a number line (VCMNA158)
    3. Recognise that the place value system can be extended to tenths and hundredths. Make connections between fractions and decimal notation (VCMNA159)

Money and financial mathematics

    1. Solve problems involving purchases and the calculation of change to the nearest five cents with and without digital technologies (VCMNA160)

Patterns and algebra

    1. Explore and describe number patterns resulting from performing multiplication (VCMNA161)
    2. Solve word problems by using number sentences involving multiplication or division where there is no remainder (VCMNA162)
    3. Use equivalent number sentences involving addition and subtraction to find unknown quantities (VCMNA163)
    4. Define a simple class of problems and solve them using an effective algorithm that involves a short sequence of steps and decisions (VCMNA164)

Measurement and Geometry

Using units of measurement

    1. Use scaled instruments to measure and compare lengths, masses, capacities and temperatures (VCMMG165)
    2. Compare objects using familiar metric units of area and volume (VCMMG166)
    3. Convert between units of time (VCMMG167)
    4. Use am and pm notation and solve simple time problems (VCMMG168)

Shape

    1. Compare the areas of regular and irregular shapes by informal means (VCMMG169)
    2. Compare and describe two dimensional shapes that result from combining and splitting common shapes, with and without the use of digital technologies (VCMMG170)
    3. Explain and compare the geometric properties of two-dimensional shapes and three-dimensional objects (VCMMG171)

Location and transformation

    1. Use simple scales, legends and directions to interpret information contained in basic maps (VCMMG172)
    2. Create symmetrical patterns, pictures and shapes with and without digital technologies (VCMMG173)

Geometric reasoning

  1. Compare angles and classify them as equal to, greater than or less than a right angle (VCMMG174)

Statistics and Probability

Chance

  1. Describe possible everyday events and order their chances of occurring (VCMSP175)
  2. Identify everyday events where one cannot happen if the other happens (VCMSP176)
  3. Identify events where the chance of one will not be affected by the occurrence of the other (VCMSP177)

Data representation and interpretation

  1. Select and trial methods for data collection, including survey questions and recording sheets (VCMSP178)
  2. Construct suitable data displays, with and without the use of digital technologies, from given or collected data. Include tables, column graphs and picture graphs where one picture can represent many data values (VCMSP179)
  3. Evaluate the effectiveness of different displays in illustrating data features including variability (VCMSP180)


Year 5 Mathematics

Number and Algebra

Number and place value

  1. Identify and describe factors and multiples of whole numbers and use them to solve problems (VCMNA181)
  2. Use estimation and rounding to check the reasonableness of answers to calculations (VCMNA182)
  3. Solve problems involving multiplication of large numbers by one- or two-digit numbers using efficient mental, written strategies and appropriate digital technologies (VCMNA183)
  4. Solve problems involving division by a one digit number, including those that result in a remainder (VCMNA184)
  5. Use efficient mental and written strategies and apply appropriate digital technologies to solve problems (VCMNA185)
  6. Recognise, represent and order numbers to at least hundreds of thousands (VCMNA186)

Fractions and decimals

  1. Compare and order common unit fractions and locate and represent them on a number line (VCMNA187)
  2. Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator (VCMNA188)
  3. Recognise that the place value system can be extended beyond hundredths (VCMNA189)
  4. Compare, order and represent decimals (VCMNA190)

Money and financial mathematics

  1. Create simple financial plans (VCMNA191)

Patterns and algebra

  1. Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction (VCMNA192)
  2. Use equivalent number sentences involving multiplication and division to find unknown quantities (VCMNA193)
  3. Follow a mathematical algorithm involving branching and repetition (iteration) (VCMNA194)

Measurement and Geometry

Using units of measurement

  1. Choose appropriate units of measurement for length, area, volume, capacity and mass (VCMMG195)
  2. Calculate the perimeter and area of rectangles and the volume and capacity of prisms using familiar metric units (VCMMG196)
  3. Compare 12- and 24-hour time systems and convert between them (VCMMG197)

Shape

  1. Connect three-dimensional objects with their nets and other two-dimensional representations (VCMMG198)

Location and transformation

  1. Use a grid reference system to describe locations. Describe routes using landmarks and directional language (VCMMG199)
  2. Describe translations, reflections and rotations of two-dimensional shapes. Identify line and rotational symmetries (VCMMG200)
  3. Apply the enlargement transformation to familiar two dimensional shapes and explore the properties of the resulting image compared with the original (VCMMG201)

Geometric reasoning

  1. Estimate, measure and compare angles using degrees. Construct angles using a protractor (VCMMG202)

Statistics and Probability

Chance

  1. List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (VCMSP203)
  2. Recognise that probabilities range from 0 to 1 (VCMSP204)

Data representation and interpretation

  1. Pose questions and collect categorical or numerical data by observation or survey (VCMSP205)
  2. Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies (VCMSP206)
  3. Describe and interpret different data sets in context (VCMSP207)


Year 6 Mathematics

Number and Algebra

Number and place value

  1. Identify and describe properties of prime, composite, square and triangular numbers (VCMNA208)
  2. Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers and make estimates for these computations (VCMNA209)
  3. Investigate everyday situations that use integers. Locate and represent these numbers on a number line (VCMNA210)

Fractions and decimals

  1. Compare fractions with related denominators and locate and represent them on a number line (VCMNA211)
  2. Solve problems involving addition and subtraction of fractions with the same or related denominators (VCMNA212)
  3. Find a simple fraction of a quantity where the result is a whole number, with and without digital technologies (VCMNA213)
  4. Add and subtract decimals, with and without digital technologies, and use estimation and rounding to check the reasonableness of answers (VCMNA214)
  5. Multiply decimals by whole numbers and perform divisions by non-zero whole numbers where the results are terminating decimals, with and without digital technologies (VCMNA215)
  6. Multiply and divide decimals by powers of 10 (VCMNA216)
  7. Make connections between equivalent fractions, decimals and percentages (VCMNA217)

Money and financial mathematics

  1. Investigate and calculate percentage discounts of 10%, 25% and 50% on sale items, with and without digital technologies (VCMNA218)

Patterns and algebra

  1. Continue and create sequences involving whole numbers, fractions and decimals. Describe the rule used to create the sequence (VCMNA219)
  2. Explore the use of brackets and order of operations to write number sentences (VCMNA220)
  3. Design algorithms involving branching and iteration to solve specific classes of mathematical problems (VCMNA221)

Measurement and Geometry

Using units of measurement

  1. Connect decimal representations to the metric system (VCMMG222)
  2. Convert between common metric units of length, mass and capacity (VCMMG223)
  3. Solve problems involving the comparison of lengths and areas using appropriate units (VCMMG224)
  4. Connect volume and capacity and their units of measurement (VCMMG225)
  5. Interpret and use timetables (VCMMG226)
  6. Measure, calculate and compare elapsed time (VCMMG227)

Shape

  1. Construct simple prisms and pyramids (VCMMG228)

Location and transformation

  1. Investigate the effect of combinations of transformations on simple and composite shapes, including creating tessellations, with and without the use of digital technologies (VCMMG229)
  2. Introduce the Cartesian coordinate system using all four quadrants (VCMMG230)

Geometric reasoning

  1. Investigate, with and without digital technologies, angles on a straight line, angles at a point and vertically opposite angles. Use results to find unknown angles (VCMMG231)

Statistics and Probability

Chance

  1. Describe probabilities using fractions, decimals and percentages (VCMSP232)
  2. Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (VCMSP233)
  3. Compare observed frequencies across experiments with expected frequencies (VCMSP234)

Data representation and interpretation

  1. Construct, interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (VCMSP235)
  2. Interpret secondary data presented in digital media and elsewhere (VCMSP236)
  3. Pose and refine questions to collect categorical or numerical data by observation or survey (VCMSP237)

 

(Source: VCAA)

Acceler8 VCE Maths Tutoring
The Mathematics Tutoring Specialist
Melbourne, Victoria, Australia.